No, it's all ultrasonics or near ultrasonic. Put a low pass filter on your music at 15k and you might not hear anything different. 90% of what we hear in tweeters is the directivity differences at 1-3khz and of course the frequency response. Plaster walls will absorb most UHF that is audible, so unless you're right in front of your speaker you may not be getting it at all.
Different materials and motors will enable the tweeter to go lower; a tweeter playing lower has wider dispersion than the woofer playing those frequencies. Different dome geometries will impact dispersion a bit as well, as will face plate shapes. Lower distortion will signal to designers that they can go lower, this is audible, but tweeter distortion isn't impacted by material as much as the motor and any efficiency gained by the waveguid
Beryllium breaks up at higher frequencies than aluminum, and I suspect diamond is even higher, but all are basically ultrasonic when they break up, even aluminum tweeters from 20 years ago.
If we're talking midranges, a beryllium makes a bit more sense but you don't see many of those.